Smoke Domain casts grayish box
This appears to be a form of z-fighting - where two faces exactly coincide. Presumably the bottom face of the Smoke Domain rests exactly on the plane. This causes Blender to have trouble in determining exactly which surface has been hit by a ray and, despite the edge of the Smoke Domain being 100% transparent, this can result in the shadow.

In order to demonstrate this effect, here's the default cube, moved 1 blender-unit up so that it's bottom face rests on the Z=0 plane with a plane added also at Z=0. The Cube has been assigned a 100% transparent shader.



And here is the render - note the square shadow of the face of the cube that should not be present :



The solution is to slightly move the Cube or the Plane so as to separate those faces - only a very slight movement is required - moving the cube only 0.00001BU up was sufficient to avoid the issue.